My Dinner with Andre

[MartinT]

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

That's probably true, but it has nothing to do with the problem.

Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you

want to address, that’s great, but I thought we had all this time
been talking about Alex’s question, which can be paraphrased as
“Given that an organism produces a particular trajectory, and that
under some conditions the velocity of motion along the trajectory at
a point is correlated with a power function of the local curvature
at that point, under what conditions does that power function take
on any particular value when the correlation is high, and what is
being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

I don't know anyone who has said it is false. I certainly haven't,

because it is demonstrably correct. It says V = V, because D is V³ /R.
It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how

long. It’s irrelevant because the V in the formula for curvature is
a purely arbitrary variable inserted only so that people can more
easily think about movement along the trajectory, and it also helps
one to visualize the concept of “angular velocity” (V(s)/R(s)).
V(s) can take on any value at any point “s” on the curve and the
algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary

V(s), but with just one observation of how some organism speeded up
and slowed down during one particular pass along the trajectory.
Since the algebra works for any V(s) at all, it is tells you nothing
about this particular V(s). We have to look elsewhere for the reason
why this V(s) happened to be the function of “s” that was observed.

Martin

···

RM: The first step in the study of how
organisms produce movement trajectories should be the
determination of whether or not the trajectories that are
observed are purposefully produced – whether or not the
movement trajectory or some aspect thereof is a controlled
variable.

                 Alex

Gomez-Marin (2016.09.07.1134)

​​

​​

                ​AGM: Rick, I really really

liked what you say in the last email until you jump
from a conscious and clear explanation onto an ad
hoc statement which is false: “** It
turns o ut**** that
there is a mathematical relationship**
between the different measures of the controlled
variable – curvature and velocity-- ** that
perfectly accounts for the “power law”
relationship** between these variables that
is observed in studies of movement
trajectories.
​”
FALSE FALSE FALSE! But you don’t care.

          RM: I do care. But no one has shown me that what I've

found is false. I would be grateful if you would try to
show me again why my derivation is false. Again, I assume
these are the formulae that can be used to compute V and
R:

          RM: Replacing V^2 in the numerator for R I end up with

the formula that everyone seems to think is wrong:

              V =

D^1/3 *R^1/3 (1)

            where

D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

          RM: I think the algebra is unquestionably correct. But

what also convinces me that this is a correct analysis is
that I have replicated all the results reported in the
power law papers using the above as the computational
formulae for V and R above and equation (1) explains all
the deviations of the observed power coefficients from
1/3.

          RM: But I would like to know why you (and nearly

everyone else apparently) thinks this mathematical
analysis is false.

[Alex_Gomez-Marin]

don’t confuse yourself and the readers again! rick, for your amazing derivation to be a power law, D should not depend mathematically on dX/dt, d2Y/dt, etc. period! aghhhhh…!!

so, again, i ask to the gurus of the revolution that will change biology and psychology and sociology: what is the organism controlling (larva and human) so as to produce such a speed-curvature constraint in the output?

···

RM: The first step in the study of how
organisms produce movement trajectories should be the
determination of whether or not the trajectories that are
observed are purposefully produced – whether or not the
movement trajectory or some aspect thereof is a controlled
variable.

                 Alex

Gomez-Marin (2016.09.07.1134)

​​

​​

                ​AGM: Rick, I really really

liked what you say in the last email until you jump
from a conscious and clear explanation onto an ad
hoc statement which is false: “** It
turns o ut**** that
there is a mathematical relationship**
between the different measures of the controlled
variable – curvature and velocity-- ** that
perfectly accounts for the “power law”
relationship** between these variables that
is observed in studies of movement
trajectories.
​”
FALSE FALSE FALSE! But you don’t care.

          RM: I do care. But no one has shown me that what I've

found is false. I would be grateful if you would try to
show me again why my derivation is false. Again, I assume
these are the formulae that can be used to compute V and
R:

          RM: Replacing V^2 in the numerator for R I end up with

the formula that everyone seems to think is wrong:

              V =

D^1/3 *R^1/3 (1)

            where

D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

          RM: I think the algebra is unquestionably correct. But

what also convinces me that this is a correct analysis is
that I have replicated all the results reported in the
power law papers using the above as the computational
formulae for V and R above and equation (1) explains all
the deviations of the observed power coefficients from
1/3.

          RM: But I would like to know why you (and nearly

everyone else apparently) thinks this mathematical
analysis is false.

[wmansell]

That’s what I’ve been trying to tell him. Great up to that point!

···

On Wed, Sep 7, 2016 at 11:18 PM, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2016.09.07.1420)]

Martin Taylor (2016.09.07.15.39)–

MT: I asked you [Martin Taylor 2016.09.06.09.10] if you would mind

providing a short form explanation of what you claim about the power
law. When I asked the question I thought I understood, but following
your two messages to Warren, I find I don’t understand at all. So
could you just give a quick, non-mathematical description of what
actually IS your explanation of the power law?

RM: Yes, I think it’s a good idea. I was trying to compose it but got waylaid. So here we go again:

RM: The first step in the study of how organisms produce movement trajectories should be the determination of whether or not the trajectories that are observed are purposefully produced – whether or not the movement trajectory or some aspect thereof is a controlled variable. This is very important because physics already has a very good explanation of non-purposefully produced movement trajectories, like those of the planets. So my analysis assumes that the movement trajectories under study are purposefully produced results of an organisms outputs.

RM: Assuming movement trajectories are controlled results of action then power law researchers are measuring two aspects of a controlled variable --its instantaneous curvature and velocity throughout the course of the movement. These two measures of the movement trajectory are presumed to represent variables involved in the production (which in PCT we take to mean control) of the movement. But we know from PCT that it is impossible to see the variables involved in keeping a controlled variable under control by simply observing the behavior of the controlled variable itself.

RM: So the observation of a fairly regular relationship between different measures of a controlled variable (in this case the “power law” relationship between curvature and velocity measures) must be due to something other than a relationship between the variable involved in producing the movement. It turns out that there is a mathematical relationship between the different measures of the controlled variable – curvature and velocity-- that perfectly accounts for the “power law” relationship between these variables that is observed in studies of movement trajectories.

RM: That’s not that quick, I’m afraid. But it’s the best I can do for now. I’ll try to hone it down as I continue to work on it. But I will say that there is a positive implication of this analysis: if you want to understand how people produce purposeful movement, stop asking what the power law suggests about how these movements are produced and start asking what variables are being controlled when people produce these movements. We know the movement is being controlled but that’s pretty general. It should be possible to develop experiments to test whether the velocity of the movement, or the curvature or both are being controlled. Or something else about the movement? And how is this control achieved.

RM: In other words, don’t go chasing illusions; study he real thing – study the fact of control.

Best

Rick

–
Richard S. Marken

“The childhood of the human race is far from over. We
have a long way to go before most people will understand that what they do for
others is just as important to their well-being as what they do for
themselves.” – William T. Powers

[wmansell]

Exactly let’s all stick with this research question please!

“Given that an organism produces a particular trajectory, and that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is high, and what is being controlled that makes this happen?”

And what is being controlled is not the two dimensional dynamic path of distance from a target. That is cheating because it just begs the question of how that target trace occurred in the first place. We need scaffolding, not skyhooks…

···

RM: The first step in the study of how
organisms produce movement trajectories should be the
determination of whether or not the trajectories that are
observed are purposefully produced – whether or not the
movement trajectory or some aspect thereof is a controlled
variable.

                 Alex

Gomez-Marin (2016.09.07.1134)

​​

​​

                ​AGM: Rick, I really really

liked what you say in the last email until you jump
from a conscious and clear explanation onto an ad
hoc statement which is false: “** It
turns o ut**** that
there is a mathematical relationship**
between the different measures of the controlled
variable – curvature and velocity-- ** that
perfectly accounts for the “power law”
relationship** between these variables that
is observed in studies of movement
trajectories.
​”
FALSE FALSE FALSE! But you don’t care.

          RM: I do care. But no one has shown me that what I've

found is false. I would be grateful if you would try to
show me again why my derivation is false. Again, I assume
these are the formulae that can be used to compute V and
R:

<mime-attachment.png>

          RM: Replacing V^2 in the numerator for R I end up with

the formula that everyone seems to think is wrong:

              V =

D^1/3 *R^1/3 (1)

            where

D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

          RM: I think the algebra is unquestionably correct. But

what also convinces me that this is a correct analysis is
that I have replicated all the results reported in the
power law papers using the above as the computational
formulae for V and R above and equation (1) explains all
the deviations of the observed power coefficients from
1/3.

          RM: But I would like to know why you (and nearly

everyone else apparently) thinks this mathematical
analysis is false.

[rsmarken]

[From Rick Marken (2016.09.08.1250)]

···

Martin Taylor (2016.09.07.23.15)–

MT: That's probably true, but it has nothing to do with the problem.

Nobody has asked how organisms produce movement trajectories. If how organisms produce particular trajectories is a problem you
want to address, that’s great, but I thought we had all this time
been talking about Alex’s question, which can be paraphrased as
“Given that an organism produces a particular trajectory, and that
under some conditions the velocity of motion along the trajectory at
a point is correlated with a power function of the local curvature
at that point, under what conditions does that power function take
on any particular value when the correlation is high, and what is
being controlled that makes this happen?”

RM: That’s packing a lot of assumptions into what I thought was Alex’s rather straightforward question which, as I recall, was “How does PCT explain the power law?”.

MT: I don’t know anyone who has said it is false.

RM: I think it was Alex, actually. You might have missed it because the word “false” was capitalized and repeated three times.

MT: I certainly haven't,

because it is demonstrably correct. It says V = V, because D is V³ /R.
It’s just irrelevant.

RM: It seems relevant to me. The power law – the phenomenon that Alex wanted explained – is found by regressing the logs of measures of curvature (R or C) against the logs of measures of velocity (V or A) that occur at the same instants during a movement trajectory. For many movement trajectories the result of this regression is a power coefficient close to 1/3 (for log R on log V) or 2/3 (for log C on log A). The equations showing the relationship between measures of R and V (and C and A) show why this is found. For example, the equation relating R to V can be written:

log (V) = 1/3log(R) + 1/3log(D)

RM: This equation shows that a regression analysis using this regression equation:

log (V) = a + b *log (R)

RM: the kind of regression analysis done to determine whether the power law applies to a movement trajectory, will find a power coefficient (b) of close to 1/3 but rarely exactly 1/3 because the variable D is left out of the regression. The extent to which the b value found by this regression deviates from 1/3 is completely predictable from knowledge of the variance of log (R) and the covariance of log (R) with log (D), both of which are measurable properties of each particular movement trajectory. It turns out that a perfect 1/3 power coefficient, b, will be found from the regression of log(R) on log (V) only for movement trajectories for which the covariatnce between log (R) with log (D) is 0.0. An example of such a movement trajectory is an ellipse.

RM: So I see my analysis as being very relevant to explaining why the power law sometimes is (and sometimes is not) observed. Whether or not the power law is found to hold for a particular movement trajectory depends on the nature of the trajectory itself, not on how it was produced or on whether it is a controlled result or not.

MT: Which is what everyone has been telling you for goodness knows how

long.

RM: I know. I can’t figure it out myself. I thought this was a PCT group, not a conventional psychologist group.

Best regards

Rick

It's irrelevant because the V in the formula for curvature is

a purely arbitrary variable inserted only so that people can more
easily think about movement along the trajectory, and it also helps
one to visualize the concept of “angular velocity” (V(s)/R(s)).
V(s) can take on any value at any point “s” on the curve and the
algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary

V(s), but with just one observation of how some organism speeded up
and slowed down during one particular pass along the trajectory.
Since the algebra works for any V(s) at all, it is tells you nothing
about this particular V(s). We have to look elsewhere for the reason
why this V(s) happened to be the function of “s” that was observed.

Martin

–
Richard S. Marken

“The childhood of the human race is far from over. We
have a long way to go before most people will understand that what they do for
others is just as important to their well-being as what they do for
themselves.” – William T. Powers

    RM: The first step in the study of how

organisms produce movement trajectories should be the
determination of whether or not the trajectories that are
observed are purposefully produced – whether or not the
movement trajectory or some aspect thereof is a controlled
variable.

          RM: But I would like to know why you (and nearly

everyone else apparently) thinks this mathematical
analysis is false.

[rsmarken]

[From Rick Marken (2016.09.08. 1300)]

···

On Wed, Sep 7, 2016 at 11:11 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: don’t confuse yourself and the readers again! rick, for your amazing derivation to be a power law, D should not depend mathematically on dX/dt, d2Y/dt, etc. period! aghhhhh…!!

RM: I don’t understand what you are saying here. See my previous post to Martin for the relevance of the D variable to the observation of the power law. I depends on having a pretty good understanding of multivariate statistical analysis. But given your background in physics and neuroscience – and since univariate statistical analysis is used to determine whether or not the power law holds for a particular movement trajectory – it should be a piece of cake for you.

AGM: so, again, i ask to the gurus of the revolution that will change biology and psychology and sociology: what is the organism controlling (larva and human) so as to produce such a speed-curvature constraint in the output?

RM: It doesn’t matter what the organism is controlling – or whether it’s controlling. The power law is a property of movement trajectories, having nothing to do with how those trajectories are produced. You will find a nice 1/3 power law, for example, for the orbits of the planets. The cause of that movement trajectory, as I’m sure you know, is gravity.

Best

Rick

On Thursday, 8 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

That's probably true, but it has nothing to do with the problem.

Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you

want to address, that’s great, but I thought we had all this time
been talking about Alex’s question, which can be paraphrased as
“Given that an organism produces a particular trajectory, and that
under some conditions the velocity of motion along the trajectory at
a point is correlated with a power function of the local curvature
at that point, under what conditions does that power function take
on any particular value when the correlation is high, and what is
being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

I don't know anyone who has said it is false. I certainly haven't,

because it is demonstrably correct. It says V = V, because D is V³ /R.
It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how

long. It’s irrelevant because the V in the formula for curvature is
a purely arbitrary variable inserted only so that people can more
easily think about movement along the trajectory, and it also helps
one to visualize the concept of “angular velocity” (V(s)/R(s)).
V(s) can take on any value at any point “s” on the curve and the
algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary

V(s), but with just one observation of how some organism speeded up
and slowed down during one particular pass along the trajectory.
Since the algebra works for any V(s) at all, it is tells you nothing
about this particular V(s). We have to look elsewhere for the reason
why this V(s) happened to be the function of “s” that was observed.

Martin

–

    RM: The first step in the study of how

organisms produce movement trajectories should be the
determination of whether or not the trajectories that are
observed are purposefully produced – whether or not the
movement trajectory or some aspect thereof is a controlled
variable.

                 Alex

Gomez-Marin (2016.09.07.1134)

​​

​​

                ​AGM: Rick, I really really

liked what you say in the last email until you jump
from a conscious and clear explanation onto an ad
hoc statement which is false: “** It
turns o ut**** that
there is a mathematical relationship**
between the different measures of the controlled
variable – curvature and velocity-- ** that
perfectly accounts for the “power law”
relationship** between these variables that
is observed in studies of movement
trajectories.
​”
FALSE FALSE FALSE! But you don’t care.

          RM: I do care. But no one has shown me that what I've

found is false. I would be grateful if you would try to
show me again why my derivation is false. Again, I assume
these are the formulae that can be used to compute V and
R:

          RM: Replacing V^2 in the numerator for R I end up with

the formula that everyone seems to think is wrong:

              V =

D^1/3 *R^1/3 (1)

            where

D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

          RM: I think the algebra is unquestionably correct. But

what also convinces me that this is a correct analysis is
that I have replicated all the results reported in the
power law papers using the above as the computational
formulae for V and R above and equation (1) explains all
the deviations of the observed power coefficients from
1/3.

          RM: But I would like to know why you (and nearly

everyone else apparently) thinks this mathematical
analysis is false.

Richard S. Marken

“The childhood of the human race is far from over. We
have a long way to go before most people will understand that what they do for
others is just as important to their well-being as what they do for
themselves.” – William T. Powers

[Huddy_Vyv]

Vyv Huddy (2016.8.9.2016)

···

[From Rick Marken (2016.09.08. 1300)]

RM: The power law is a property of movement trajectories, having nothing to do with how those trajectories are produced. You will find a nice 1/3 power law, for example, for the orbits of the planets. The cause of that movement trajectory, as I’m sure
you know, is gravity.

VH: Not sure about that the orbital speed of Mercury is faster than that of planets further out? Which gradually move more slowly? That is velocity is lower with increasing curvature?

http://nssdc.gsfc.nasa.gov/planetary/factsheet/

VH: Is this to with Kepler’s third law, which the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit? So I think
this is the opposite of the biological power law?

Best

Rick

On Thursday, 8 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

RM: The first step in the study of how organisms produce movement trajectories should be the determination of whether or not the trajectories that are observed are purposefully produced – whether or not the movement trajectory or some
aspect thereof is a controlled variable.

That’s probably true, but it has nothing to do with the problem. Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you want to address, that’s great, but I thought we had all this time been talking about Alex’s question, which can be paraphrased as “Given that an organism produces a particular trajectory, and
that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is
high, and what is being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

Alex Gomez-Marin (2016.09.07.1134)

AGM: Rick, I really really liked what you say in the last email until you jump from a conscious and clear explanation onto an ad hoc statement which is false: "It turns out that there is a mathematical relationship between the different measures of the controlled variable – curvature and velocity–
that perfectly accounts for the “power law” relationship between these variables that is observed in studies of movement trajectories.
" FALSE FALSE FALSE! But you don’t care.

RM: I do care. But no one has shown me that what I’ve found is false. I would be grateful if you would try to show me again why my derivation is false. Again, I assume these are the formulae that can be used to compute V and R:

RM: Replacing V^2 in the numerator for R I end up with the formula that everyone seems to think is wrong:

V = D^1/3 *R^1/3 (1)

where D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

RM: I think the algebra is unquestionably correct. But what also convinces me that this is a correct analysis is that I have replicated all the results reported in the power law papers using the above as the computational formulae for V and R above and
equation (1) explains all the deviations of the observed power coefficients from 1/3.

RM: But I would like to know why you (and nearly everyone else apparently) thinks this mathematical analysis is false.

I don’t know anyone who has said it is false. I certainly haven’t, because it is demonstrably correct. It says V = V, because D is V³/R. It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how long. It’s irrelevant because the V in the formula for curvature is a purely arbitrary variable inserted only so that people can more easily think about movement along the trajectory, and it
also helps one to visualize the concept of “angular velocity” (V(s)/R(s)). V(s) can take on any value at any point “s” on the curve and the algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary V(s), but with just one observation of how some organism speeded up and slowed down during one particular pass along the trajectory. Since the algebra works for any V(s) at all, it is tells
you nothing about this particular V(s). We have to look elsewhere for the reason why this V(s) happened to be the function of “s” that was observed.

Martin

–
Richard S. Marken

“The childhood of the human race is far from over. We have a long way to go before most people will understand that what they do for others is just as important to their well-being as what they do for themselves.” – William T. Powers

[Huddy_Vyv]

VH: Sorry! The planets velocity is higher with increasing curvature! This is dangerous topic?!

···

---

From: Huddy, Vyv
Sent: 08 September 2016 21:18
To: csgnet@lists.illinois.edu
Subject: Re: My Dinner with Andre

Vyv Huddy (2016.8.9.2016)

[From Rick Marken (2016.09.08. 1300)]

RM: The power law is a property of movement trajectories, having nothing to do with how those trajectories are produced. You will find a nice 1/3 power law, for example, for the orbits of the planets. The cause of that movement trajectory, as I’m sure
you know, is gravity.

VH: Not sure about that the orbital speed of Mercury is faster than that of planets further out? Which gradually move more slowly? That is velocity is lower with increasing curvature?

http://nssdc.gsfc.nasa.gov/planetary/factsheet/

VH: Is this to with Kepler’s third law, which the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit? So I think this
is the opposite of the biological power law?

Best

Rick

On Thursday, 8 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

RM: The first step in the study of how organisms produce movement trajectories should be the determination of whether or not the trajectories that are observed are purposefully produced – whether or not the movement trajectory or some
aspect thereof is a controlled variable.

That’s probably true, but it has nothing to do with the problem. Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you want to address, that’s great, but I thought we had all this time been talking about Alex’s question, which can be paraphrased as “Given that an organism produces a particular trajectory, and
that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is
high, and what is being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

Alex Gomez-Marin (2016.09.07.1134)

AGM: Rick, I really really liked what you say in the last email until you jump from a conscious and clear explanation onto an ad hoc statement which is false: "It turns out that there is a mathematical relationship between the different measures of the controlled variable – curvature and velocity–
that perfectly accounts for the “power law” relationship between these variables that is observed in studies of movement trajectories.
" FALSE FALSE FALSE! But you don’t care.

RM: I do care. But no one has shown me that what I’ve found is false. I would be grateful if you would try to show me again why my derivation is false. Again, I assume these are the formulae that can be used to compute V and R:

RM: Replacing V^2 in the numerator for R I end up with the formula that everyone seems to think is wrong:

V = D^1/3 *R^1/3 (1)

where D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

RM: I think the algebra is unquestionably correct. But what also convinces me that this is a correct analysis is that I have replicated all the results reported in the power law papers using the above as the computational formulae for V and R above and
equation (1) explains all the deviations of the observed power coefficients from 1/3.

RM: But I would like to know why you (and nearly everyone else apparently) thinks this mathematical analysis is false.

I don’t know anyone who has said it is false. I certainly haven’t, because it is demonstrably correct. It says V = V, because D is V³/R. It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how long. It’s irrelevant because the V in the formula for curvature is a purely arbitrary variable inserted only so that people can more easily think about movement along the trajectory, and it
also helps one to visualize the concept of “angular velocity” (V(s)/R(s)). V(s) can take on any value at any point “s” on the curve and the algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary V(s), but with just one observation of how some organism speeded up and slowed down during one particular pass along the trajectory. Since the algebra works for any V(s) at all, it is tells
you nothing about this particular V(s). We have to look elsewhere for the reason why this V(s) happened to be the function of “s” that was observed.

Martin

–
Richard S. Marken

“The childhood of the human race is far from over. We have a long way to go before most people will understand that what they do for others is just as important to their well-being as what they do for themselves.” – William T. Powers

[Alex_Gomez-Marin]

[From Alex Gomez-Marin (2016.09.08. 2244)]

AGM: Rick, that is what you are doing with your derivation. Let’s suppose that Y=aX^3 (I just made up this equation). Now you say that d=aX and write Y=d*X^2, so then you think you proved that there is a power-law of exponent 2 between Y and X?! If so, then you can rearrange any equation by defining a term “d”, then forget that it is NOT a constant, and get whatever Y-X relation.

AGM: And, yes, my original question is what Martin just rephrased. But if you think your kindergarten flawed mathematics combined with the ad hoc decision that any power-law is more than an illusion, but a phenomenon not worthy of study, then why all this fuzz?

AGM: One thing is clear, given the empirical non-trivial relation between speed and curvature found in humans for more than 40 years now, and my recent discovery in another species (the fly), there is a huge opportunity to find out the perceptual origin of that motor relation.

···

On Thu, Sep 8, 2016 at 10:20 PM, Huddy, Vyv v.huddy@ucl.ac.uk wrote:

VH: Sorry! The planets velocity is higher with increasing curvature! This is dangerous topic?!

---

From: Huddy, Vyv
Sent: 08 September 2016 21:18
To: csgnet@lists.illinois.edu
Subject: Re: My Dinner with Andre

Vyv Huddy (2016.8.9.2016)

[From Rick Marken (2016.09.08. 1300)]

RM: The power law is a property of movement trajectories, having nothing to do with how those trajectories are produced. You will find a nice 1/3 power law, for example, for the orbits of the planets. The cause of that movement trajectory, as I’m sure
you know, is gravity.

VH: Not sure about that the orbital speed of Mercury is faster than that of planets further out? Which gradually move more slowly? That is velocity is lower with increasing curvature?

http://nssdc.gsfc.nasa.gov/planetary/factsheet/

VH: Is this to with Kepler’s third law, which the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit? So I think this
is the opposite of the biological power law?

Best

Rick

On Thursday, 8 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

That’s probably true, but it has nothing to do with the problem. Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you want to address, that’s great, but I thought we had all this time been talking about Alex’s question, which can be paraphrased as “Given that an organism produces a particular trajectory, and
that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is
high, and what is being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

I don’t know anyone who has said it is false. I certainly haven’t, because it is demonstrably correct. It says V = V, because D is V³/R. It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how long. It’s irrelevant because the V in the formula for curvature is a purely arbitrary variable inserted only so that people can more easily think about movement along the trajectory, and it
also helps one to visualize the concept of “angular velocity” (V(s)/R(s)). V(s) can take on any value at any point “s” on the curve and the algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary V(s), but with just one observation of how some organism speeded up and slowed down during one particular pass along the trajectory. Since the algebra works for any V(s) at all, it is tells
you nothing about this particular V(s). We have to look elsewhere for the reason why this V(s) happened to be the function of “s” that was observed.

Martin

–
Richard S. Marken

“The childhood of the human race is far from over. We have a long way to go before most people will understand that what they do for others is just as important to their well-being as what they do for themselves.” – William T. Powers

RM: The first step in the study of how organisms produce movement trajectories should be the determination of whether or not the trajectories that are observed are purposefully produced – whether or not the movement trajectory or some
aspect thereof is a controlled variable.

Alex Gomez-Marin (2016.09.07.1134)

AGM: Rick, I really really liked what you say in the last email until you jump from a conscious and clear explanation onto an ad hoc statement which is false: "It turns out that there is a mathematical relationship between the different measures of the controlled variable – curvature and velocity–
that perfectly accounts for the “power law” relationship between these variables that is observed in studies of movement trajectories.
" FALSE FALSE FALSE! But you don’t care.

RM: I do care. But no one has shown me that what I’ve found is false. I would be grateful if you would try to show me again why my derivation is false. Again, I assume these are the formulae that can be used to compute V and R:

RM: Replacing V^2 in the numerator for R I end up with the formula that everyone seems to think is wrong:

V = D^1/3 *R^1/3 (1)

where D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

RM: I think the algebra is unquestionably correct. But what also convinces me that this is a correct analysis is that I have replicated all the results reported in the power law papers using the above as the computational formulae for V and R above and
equation (1) explains all the deviations of the observed power coefficients from 1/3.

RM: But I would like to know why you (and nearly everyone else apparently) thinks this mathematical analysis is false.

[MartinT]

[Martin Taylor 2016.09.08.17.21]

[From Rick Marken (2016.09.08.1250)]

"The power law" has nothing to do with how organisms produce

movement trajectories. At least teh power law of interest to Alex
doesn’t.

​​

​​

I guess you read Alex's words as carefully as you read mine. Here's

the quote from Alex: " “** It
turns o ut**** that
there is a mathematical relationship** between the different
measures of the controlled variable – curvature and velocity-- ** that
perfectly accounts for the “power law” relationship** between
these variables that is observed in studies of movement
trajectories.
​” FALSE FALSE
FALSE! But you don’t care."

  I looove how you read this as saying that your mathematical

analysis is false. To help you, Alex bolded “that perfectly
accounts for…”.

Let's follow the logic here, since this equation is correct for

every value of V, since 1/3log(D) = log(V) - 1/3log(R).

A house was burgled, and a camera showed that the burglar had two

feet. I notice a man on the street who has two feet, and call the
cops to arrest him, because obviously, having two feet, he must have
been the burglar.

An organism moved along a trajectory, and its velocity on the curves

depended on the sharpness of the curves in a way I measured. I
notice that the velocity I measured satisfies the equation
reasonably closely. Therefore the equation accounts for the velocity
with which the organism moved at different points along its path.

Or: Socrates is a man. Socrates is wise. It follows that all men are

wise.

Martin

···

Martin Taylor (2016.09.07.23.15)–

            MT: That's probably true, but it has nothing to

do with the problem. Nobody has asked how organisms
produce movement trajectories. If how organisms produce
particular trajectories is a problem you want to
address, that’s great, but I thought we had all this
time been talking about Alex’s question, which can be
paraphrased as “Given that an organism produces a
particular trajectory, and that under some conditions
the velocity of motion along the trajectory at a point
is correlated with a power function of the local
curvature at that point, under what conditions does that
power function take on any particular value when the
correlation is high, and what is being controlled that
makes this happen?”

          RM: That's packing a lot of assumptions into what I

thought was Alex’s rather straightforward question which,
as I recall, was “How does PCT explain the power law?”.

                  RM: The first step in the

study of how organisms produce movement
trajectories should be the determination of
whether or not the trajectories that are observed
are purposefully produced – whether or not the
movement trajectory or some aspect thereof is a
controlled variable.

MT: I don’t know anyone who has said it is false.

          RM: I think it was Alex, actually. You might have

missed it because the word “false” was capitalized and
repeated three times.

                        RM: But I would like to know why you (and

nearly everyone else apparently) thinks this
mathematical analysis is false.

            MT: I certainly haven't, because it

is demonstrably correct. It says V = V, because D is V³ /R.
It’s just irrelevant.

          RM: It seems relevant to me. The power law -- the

phenomenon that Alex wanted explained – is found by
regressing the logs of measures of curvature (R or C)
against the logs of measures of velocity (V or A) that
occur at the same instants during a movement trajectory.
For many movement trajectories the result of this
regression is a power coefficient close to 1/3 (for log R
on log V) or 2/3 (for log C on log A). The equations
showing the relationship between measures of R and V (and
C and A) show why this is found. For example, the equation
relating R to V can be written:

log (V) = 1/3log(R) + 1/3log(D)

[rsmarken]

[From Rick Marken (2016.09.08.1500)]

···

Vyv Huddy (2016.8.9.2016)

RM: Yes, orbital velocity decreases as you move from the inner to outer planets. But to the extent that the orbits are perfectly elliptical each of the orbits themselves will follow the 1/3 (and 2/3) power law perfectly.

Best

Rick

–

RM: The power law is a property of movement trajectories, having nothing to do with how those trajectories are produced. You will find a nice 1/3 power law, for example, for the orbits of the planets. The cause of that movement trajectory, as I’m sure
you know, is gravity.

VH: Not sure about that the orbital speed of Mercury is faster than that of planets further out? Which gradually move more slowly? That is velocity is lower with increasing curvature?

http://nssdc.gsfc.nasa.gov/planetary/factsheet/

VH: Is this to with Kepler’s third law, which the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit? So I think
this is the opposite of the biological power law?

Best

Rick

On Thursday, 8 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

That’s probably true, but it has nothing to do with the problem. Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you want to address, that’s great, but I thought we had all this time been talking about Alex’s question, which can be paraphrased as “Given that an organism produces a particular trajectory, and
that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is
high, and what is being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

I don’t know anyone who has said it is false. I certainly haven’t, because it is demonstrably correct. It says V = V, because D is V³/R. It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how long. It’s irrelevant because the V in the formula for curvature is a purely arbitrary variable inserted only so that people can more easily think about movement along the trajectory, and it
also helps one to visualize the concept of “angular velocity” (V(s)/R(s)). V(s) can take on any value at any point “s” on the curve and the algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary V(s), but with just one observation of how some organism speeded up and slowed down during one particular pass along the trajectory. Since the algebra works for any V(s) at all, it is tells
you nothing about this particular V(s). We have to look elsewhere for the reason why this V(s) happened to be the function of “s” that was observed.

Martin

–
Richard S. Marken

“The childhood of the human race is far from over. We have a long way to go before most people will understand that what they do for others is just as important to their well-being as what they do for themselves.” – William T. Powers

RM: The first step in the study of how organisms produce movement trajectories should be the determination of whether or not the trajectories that are observed are purposefully produced – whether or not the movement trajectory or some
aspect thereof is a controlled variable.

Alex Gomez-Marin (2016.09.07.1134)

AGM: Rick, I really really liked what you say in the last email until you jump from a conscious and clear explanation onto an ad hoc statement which is false: "It turns out that there is a mathematical relationship between the different measures of the controlled variable – curvature and velocity–
that perfectly accounts for the “power law” relationship between these variables that is observed in studies of movement trajectories.
" FALSE FALSE FALSE! But you don’t care.

RM: I do care. But no one has shown me that what I’ve found is false. I would be grateful if you would try to show me again why my derivation is false. Again, I assume these are the formulae that can be used to compute V and R:

RM: Replacing V^2 in the numerator for R I end up with the formula that everyone seems to think is wrong:

V = D^1/3 *R^1/3 (1)

where D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

RM: I think the algebra is unquestionably correct. But what also convinces me that this is a correct analysis is that I have replicated all the results reported in the power law papers using the above as the computational formulae for V and R above and
equation (1) explains all the deviations of the observed power coefficients from 1/3.

RM: But I would like to know why you (and nearly everyone else apparently) thinks this mathematical analysis is false.

Richard S. Marken

“The childhood of the human race is far from over. We
have a long way to go before most people will understand that what they do for
others is just as important to their well-being as what they do for
themselves.” – William T. Powers

[Alex_Gomez-Marin]

agh…! rick, if i showed to you that planet orbits don’t follow the power law, you could not care less because you are the prophet whose job is to repeat the mantra regardless of basic math confusion and even regardless of evidence. this is very annoying!

···

Vyv Huddy (2016.8.9.2016)

RM: Yes, orbital velocity decreases as you move from the inner to outer planets. But to the extent that the orbits are perfectly elliptical each of the orbits themselves will follow the 1/3 (and 2/3) power law perfectly.

Best

Rick

–
Richard S. Marken

“The childhood of the human race is far from over. We
have a long way to go before most people will understand that what they do for
others is just as important to their well-being as what they do for
themselves.” – William T. Powers

RM: The power law is a property of movement trajectories, having nothing to do with how those trajectories are produced. You will find a nice 1/3 power law, for example, for the orbits of the planets. The cause of that movement trajectory, as I’m sure
you know, is gravity.

VH: Not sure about that the orbital speed of Mercury is faster than that of planets further out? Which gradually move more slowly? That is velocity is lower with increasing curvature?

http://nssdc.gsfc.nasa.gov/planetary/factsheet/

VH: Is this to with Kepler’s third law, which the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit? So I think
this is the opposite of the biological power law?

Best

Rick

On Thursday, 8 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

That’s probably true, but it has nothing to do with the problem. Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you want to address, that’s great, but I thought we had all this time been talking about Alex’s question, which can be paraphrased as “Given that an organism produces a particular trajectory, and
that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is
high, and what is being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

I don’t know anyone who has said it is false. I certainly haven’t, because it is demonstrably correct. It says V = V, because D is V³/R. It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how long. It’s irrelevant because the V in the formula for curvature is a purely arbitrary variable inserted only so that people can more easily think about movement along the trajectory, and it
also helps one to visualize the concept of “angular velocity” (V(s)/R(s)). V(s) can take on any value at any point “s” on the curve and the algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary V(s), but with just one observation of how some organism speeded up and slowed down during one particular pass along the trajectory. Since the algebra works for any V(s) at all, it is tells
you nothing about this particular V(s). We have to look elsewhere for the reason why this V(s) happened to be the function of “s” that was observed.

Martin

–
Richard S. Marken

“The childhood of the human race is far from over. We have a long way to go before most people will understand that what they do for others is just as important to their well-being as what they do for themselves.” – William T. Powers

RM: The first step in the study of how organisms produce movement trajectories should be the determination of whether or not the trajectories that are observed are purposefully produced – whether or not the movement trajectory or some
aspect thereof is a controlled variable.

Alex Gomez-Marin (2016.09.07.1134)

AGM: Rick, I really really liked what you say in the last email until you jump from a conscious and clear explanation onto an ad hoc statement which is false: "It turns out that there is a mathematical relationship between the different measures of the controlled variable – curvature and velocity–
that perfectly accounts for the “power law” relationship between these variables that is observed in studies of movement trajectories.
" FALSE FALSE FALSE! But you don’t care.

RM: I do care. But no one has shown me that what I’ve found is false. I would be grateful if you would try to show me again why my derivation is false. Again, I assume these are the formulae that can be used to compute V and R:

RM: Replacing V^2 in the numerator for R I end up with the formula that everyone seems to think is wrong:

V = D^1/3 *R^1/3 (1)

where D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

RM: I think the algebra is unquestionably correct. But what also convinces me that this is a correct analysis is that I have replicated all the results reported in the power law papers using the above as the computational formulae for V and R above and
equation (1) explains all the deviations of the observed power coefficients from 1/3.

RM: But I would like to know why you (and nearly everyone else apparently) thinks this mathematical analysis is false.

[rsmarken]

[From Rick Marken (2016.09.08.1850)]

···

Alex Gomez-Marin (2016.09.08. 2244)

AGM: Rick, that is what you are doing with your derivation. Let’s suppose that Y=aX^3 (I just made up this equation). Now you say that d=aX and write Y=d*X^2, so then you think you proved that there is a power-law of exponent 2 between Y and X?! If so, then you can rearrange any equation by defining a term “d”, then forget that it is NOT a constant, and get whatever Y-X relation.

RM: It’s not quite the same as what I do. I didn’t factor d out of another expression. But I can use your equation as an analogy to the problem with the power law. You new expression can be written as a linear equation by taking the log of both sides:

log (Y) = 1.0* log (d) + 3 * log(X)

RM: To make this analogous to the power law case we will make a variable along with X so that d is the product of two variables: d = X * a. Now let’s say some researchers have reason to believe that there is a power relationship between d and Y with a coefficient that is >1.0. So they measure d and Y and do a log-log regression using the following regression equation:

log (Y) = a + b*log(d)

RM: What they will find is that the coefficient, b, of log (d) is always > 1.0. The regression always gives a biased estimate of the coefficient of d (1.0) because Y is a function of both d and X. So leaving X out of the regression equation results in the wrong estimate of the true coefficient of d, which is 1.0.

RM: This is exactly analogous to what is happening in the case of the power law. The true relationship (in linear form) between R and V is:

log (V) = 1/3* log(R) + 1/3*log(V^3/R)

RM: In this case I’ve written D as V^3/R since that way R shows up as part of both predictor variables. Power law researchers are doing this regression using only the variable R:

log (V) = a + b*log(R)

RM: The result is that they are getting a biased estimate of the true value of the coefficient of R, which s 1/3. The regression using only R as a predictor will give an accurate estimate of this coefficient – 1/3 – only for data (trajectories) where the covariance of R with V^3/R (the variable formerly known as D) is 0.0.

AGM: And, yes, my original question is what Martin just rephrased.

RM: Well, then it’s not a good question because it makes an assumption that goes beyond the data (the data being the power law). The assumption it makes is that the observed phenomenon is a result of controlling some variable. But there is no evidence in the data that control is going on.

AGM: But if you think your kindergarten flawed mathematics combined with the ad hoc decision that any power-law is more than an illusion, but a phenomenon not worthy of study, then why all this fuzz?

RM: Because power law researchers interpret the power law as a slowing of action in response to increased curvature when it’s not. They are succumbing to a version of the behavioral illusion and developing complex mathematical models to explain why action slows at curves when this is not what is actually happening. A control theory analysis of the situation shows that this couldn’t be what they are seeing (you can’t see the disturbance – curvature-- and the reaction to that disturbance – velocity – in the variations of a single variable) and my statistical analysis shows what they actually are seeing.

AGM: One thing is clear, given the empirical non-trivial relation between speed and curvature found in humans for more than 40 years now, and my recent discovery in another species (the fly), there is a huge opportunity to find out the perceptual origin of that motor relation.

RM: But both Kent and I have presented the perceptual control model that produces movement trajectories that result in a power law relationship between curvature and velocity. It’s just that no body seemed to like it. Well, they did like it when Kent presented it but they like Kent better than me;-)

Best regards

Rick

–
Richard S. Marken

“The childhood of the human race is far from over. We
have a long way to go before most people will understand that what they do for
others is just as important to their well-being as what they do for
themselves.” – William T. Powers

VH: Sorry! The planets velocity is higher with increasing curvature! This is dangerous topic?!

---

From: Huddy, Vyv
Sent: 08 September 2016 21:18
To: csgnet@lists.illinois.edu
Subject: Re: My Dinner with Andre

Vyv Huddy (2016.8.9.2016)

[From Rick Marken (2016.09.08. 1300)]

RM: The power law is a property of movement trajectories, having nothing to do with how those trajectories are produced. You will find a nice 1/3 power law, for example, for the orbits of the planets. The cause of that movement trajectory, as I’m sure
you know, is gravity.

VH: Not sure about that the orbital speed of Mercury is faster than that of planets further out? Which gradually move more slowly? That is velocity is lower with increasing curvature?

http://nssdc.gsfc.nasa.gov/planetary/factsheet/

VH: Is this to with Kepler’s third law, which the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit? So I think this
is the opposite of the biological power law?

Best

Rick

On Thursday, 8 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

That’s probably true, but it has nothing to do with the problem. Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you want to address, that’s great, but I thought we had all this time been talking about Alex’s question, which can be paraphrased as “Given that an organism produces a particular trajectory, and
that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is
high, and what is being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

I don’t know anyone who has said it is false. I certainly haven’t, because it is demonstrably correct. It says V = V, because D is V³/R. It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how long. It’s irrelevant because the V in the formula for curvature is a purely arbitrary variable inserted only so that people can more easily think about movement along the trajectory, and it
also helps one to visualize the concept of “angular velocity” (V(s)/R(s)). V(s) can take on any value at any point “s” on the curve and the algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary V(s), but with just one observation of how some organism speeded up and slowed down during one particular pass along the trajectory. Since the algebra works for any V(s) at all, it is tells
you nothing about this particular V(s). We have to look elsewhere for the reason why this V(s) happened to be the function of “s” that was observed.

Martin

–
Richard S. Marken

“The childhood of the human race is far from over. We have a long way to go before most people will understand that what they do for others is just as important to their well-being as what they do for themselves.” – William T. Powers

RM: The first step in the study of how organisms produce movement trajectories should be the determination of whether or not the trajectories that are observed are purposefully produced – whether or not the movement trajectory or some
aspect thereof is a controlled variable.

Alex Gomez-Marin (2016.09.07.1134)

AGM: Rick, I really really liked what you say in the last email until you jump from a conscious and clear explanation onto an ad hoc statement which is false: "It turns out that there is a mathematical relationship between the different measures of the controlled variable – curvature and velocity–
that perfectly accounts for the “power law” relationship between these variables that is observed in studies of movement trajectories.
" FALSE FALSE FALSE! But you don’t care.

RM: I do care. But no one has shown me that what I’ve found is false. I would be grateful if you would try to show me again why my derivation is false. Again, I assume these are the formulae that can be used to compute V and R:

RM: Replacing V^2 in the numerator for R I end up with the formula that everyone seems to think is wrong:

V = D^1/3 *R^1/3 (1)

where D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

RM: I think the algebra is unquestionably correct. But what also convinces me that this is a correct analysis is that I have replicated all the results reported in the power law papers using the above as the computational formulae for V and R above and
equation (1) explains all the deviations of the observed power coefficients from 1/3.

RM: But I would like to know why you (and nearly everyone else apparently) thinks this mathematical analysis is false.

[rsmarken]

[From Rick Marken (2016.09.10.1450)]

···

On Wed, Sep 7, 2016 at 11:45 PM, Warren Mansell wmansell@gmail.com wrote:

WM: Exactly let’s all stick with this research question please!

“Given that an organism produces a particular trajectory, and that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is high, and what is being controlled that makes this happen?”

RM: Except for that last phase, that’s the research question I have answered (even if you don’t like the answer, it is an answer to that question). That last part – “what is being controlled that makes this happen?”-- assumes that the explanation is in terms of what variable is being controlled. However, there is no reason to believe that control has anything to do with the observation of the power law. There is nothing in the power law that suggests that a variable is being maintained in a reference state (constant or variable) protected from disturbance.

WM: And what is being controlled is not the two dimensional dynamic path of distance from a target.

RM: How do you know? Actually, it seems highly likely that it’s precisely this dynamic path that is being controlled when people produce movement trajectories. Physics suggests that these trajectories are being produced in the face of disturbances. If it’s not the trajectories themselves that are controlled then what else could it be?

WM: That is cheating because it just begs the question of how that target trace occurred in the first place. We need scaffolding, not skyhooks…

RM: I think you mean that assuming that an observed movement trajectory is the result of a dynamically varying reference for the position of the moved entity (such as a cursor) is begging the question. But I don’t think it is. It’s proposing a falsifiable theory that explains what is observed. The theory can be disproved by seeing whether it can account for the movement trajectory when disturbances are applied to the moved entity. I have done this, using a cursor as the moved entity and taking the observed movement of the cursor under disturbance as a reflection of the movement of the reference for cursor position. When this estimate of the reference is placed in a control model, moving the cursor in the face of the same disturbances that had been present when the person had moved the cursor, the model behaved exactly the same as the person. This would not have happened if the position of the cursor were not a controlled variable being controlled relative to the estimates reference.

RM: So according to my model (PCT) what we are seeing when people make two dimensional movements of a cursor on the screen is the dynamically varying reference state of cursor position. I’m sure this same model would apply to the movements made during cursive writing or when spacial patterns are traced out by moving a finger through space. Most of these movements will produce “power law” relationships between curvature and velocity with coefficients close to 1/3 (or 2/3) for the reasons given in my statistical analysis of the power law.

Best

Rick

On 8 Sep 2016, at 07:11, Alex Gomez-Marin agomezmarin@gmail.com wrote:

don’t confuse yourself and the readers again! rick, for your amazing derivation to be a power law, D should not depend mathematically on dX/dt, d2Y/dt, etc. period! aghhhhh…!!

so, again, i ask to the gurus of the revolution that will change biology and psychology and sociology: what is the organism controlling (larva and human) so as to produce such a speed-curvature constraint in the output?

On Thursday, 8 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

That's probably true, but it has nothing to do with the problem.

Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you

want to address, that’s great, but I thought we had all this time
been talking about Alex’s question, which can be paraphrased as
“Given that an organism produces a particular trajectory, and that
under some conditions the velocity of motion along the trajectory at
a point is correlated with a power function of the local curvature
at that point, under what conditions does that power function take
on any particular value when the correlation is high, and what is
being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

I don't know anyone who has said it is false. I certainly haven't,

because it is demonstrably correct. It says V = V, because D is V³ /R.
It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how

long. It’s irrelevant because the V in the formula for curvature is
a purely arbitrary variable inserted only so that people can more
easily think about movement along the trajectory, and it also helps
one to visualize the concept of “angular velocity” (V(s)/R(s)).
V(s) can take on any value at any point “s” on the curve and the
algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary

V(s), but with just one observation of how some organism speeded up
and slowed down during one particular pass along the trajectory.
Since the algebra works for any V(s) at all, it is tells you nothing
about this particular V(s). We have to look elsewhere for the reason
why this V(s) happened to be the function of “s” that was observed.

Martin

–
Richard S. Marken

“The childhood of the human race is far from over. We
have a long way to go before most people will understand that what they do for
others is just as important to their well-being as what they do for
themselves.” – William T. Powers

    RM: The first step in the study of how

organisms produce movement trajectories should be the
determination of whether or not the trajectories that are
observed are purposefully produced – whether or not the
movement trajectory or some aspect thereof is a controlled
variable.

                 Alex

Gomez-Marin (2016.09.07.1134)

​​

​​

                ​AGM: Rick, I really really

liked what you say in the last email until you jump
from a conscious and clear explanation onto an ad
hoc statement which is false: “** It
turns o ut**** that
there is a mathematical relationship**
between the different measures of the controlled
variable – curvature and velocity-- ** that
perfectly accounts for the “power law”
relationship** between these variables that
is observed in studies of movement
trajectories.
​”
FALSE FALSE FALSE! But you don’t care.

          RM: I do care. But no one has shown me that what I've

found is false. I would be grateful if you would try to
show me again why my derivation is false. Again, I assume
these are the formulae that can be used to compute V and
R:

<mime-attachment.png>

          RM: Replacing V^2 in the numerator for R I end up with

the formula that everyone seems to think is wrong:

              V =

D^1/3 *R^1/3 (1)

            where

D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

          RM: I think the algebra is unquestionably correct. But

what also convinces me that this is a correct analysis is
that I have replicated all the results reported in the
power law papers using the above as the computational
formulae for V and R above and equation (1) explains all
the deviations of the observed power coefficients from
1/3.

          RM: But I would like to know why you (and nearly

everyone else apparently) thinks this mathematical
analysis is false.

[_Boris_Hartman]

Bellow in text…

···

From: Richard Marken [mailto:rsmarken@gmail.com]
Sent: Tuesday, September 06, 2016 3:50 AM
To: csgnet@lists.illinois.edu
Subject: Re: My Dinner with Andre

[From RIck Marken (2016.09.05.1850)]

Vyv Huddy (2211.05.09.2016)–

RM: If the movement is purposeful then, due to disturbances, the actions that produce the observed movement trajectory will be quite different than the movement itself.

VH: What are the disturbances referred to here? I looked at the spreadsheet model and couldn’t find these? Perhaps I misunderstanding what’s included there but I thought it was the PCT model in the figure? In the figure the disturbances are environmental but if someone is drawing on a flat stable surface then I’m not sure what they might be?

RM: Disturbances are variations in environmental variables that affect controlled variables independently of the effect that the system has on these variables. When you are drawing (or writing) on a flat, stable surface the controlled variable is the X, Y position of the pen tip. Disturbances to that variable are things like variations in the texture of the paper, in the wetness of the pen tip, in the the push-down force you are exerting on the pen; variations in any physical variables that affect the movement of the pen across the paper. In the spreadsheet model the disturbances are the variables dx and dy, which affect the position of the cursor (variables X and Y) for both the person and the model.

RM: All behavior is produced in a disturbance prone world.

HB : There are also behaviors which are not result of disturbances in »prone world« (unintentional movements, tremor, etc….). But it maybe could help if yoou clarify »disturbances in prone world« ???

RM : A causal model can’t behave in such a world like an organism does.

HB : Right.

RM : PCT is the only model that can behave like an organism does in the real world of unpredictable (and typically invisible) disturbances.

HB : PCT could be the only model that can behave like an organism. I suppose that my 50 x explanation to you started to work. The problem is that model of overall organism on p. 191 in B:CP is not finished yet (it’s rather confused)

….and so PCT can not yet answer propperly how organisms behave. One of »blind ways« in explaining this is also RCT (Rick’s Control Theory).

RM : It does this, of course, by controlling its inputs rather than its outputs.

HB : What did you want to say here ? That organism controls its inputs with behavior (ouput) ??? So you think that output is controlled ???

Best,

Boris

Best

Rick

VH: I can understand a distrubance be at higher levels perception, like a reference to perceive elipse configuration might be disturbed by a blank piece of paper I think?? If the instruction is to draw an elipse?

So what you are looking at when you see a movement trajectory (if it is intentionally produced) is variations in a variable that are the combined result of the actions of the system and disturbances to that variable. So you can’t tell anything about the actions that produced the movement by just looking at the movement itself.

RM: It was this understanding about the nature of control that led to my mathematical analysis of the power law. Power law researchers are “looking at” only the movement that is being produced – “looking at” it in terms of measures of curvature and velocity – and thinking that one measure is an independent variable (curvature) and the other a dependent variable (velocity). But according to control theory the independent and dependent variables that result in a purposeful movement trajectories (disturbance and output) are not visible in the movement trajectories themselves. So a control theory analysis would lead one to expect that there would be no relationship at all between any two measures of intentionally produced movement trajectories. Yet, power law researchers do observe a fairly regular relationship between measures of curvature and velocity in many movement trajectories; the relationship is a 1/3 power law when curvature and velocity are measured as R and V, respectively, and a 2/3 power law when curvature and velocity are measured as C and A, respectively.

RM: It was this surprising fact – that a nice power law relationship was found where control theory says it should not be found (as well as the fact that this power law is also found for unintentionally produced movement trajectories, like the movements of the planets) – that led me to suspect that the power law might be a mathematical property of the relationship between the measures of curvature and velocity that are used in power law research. After all, the power law is found using regression analysis with measures of curvature as the predictor variable and measures of velocity as the criterion variable in the analysis. If there is a mathematical relationship between the measures of curvature and velocity used in power law research the regression analysis will pick this up.

RM: So I looked at the equations for computing the values of R (curvature) and V (velocity) in power law research and discovered that there was indeed a mathematical relationship between these variables (and correspondingly between curvature measured as C and velocity measured as A). And the mathematical relationship is a power relationship with a 1/3 power coefficient for the relationship between R and V and a 2/3 power coefficient for the relationship between C and A, exactly the values that power law researchers have been finding for many movement trajectories. Coincidence? I didn’t think so. But power law researchers don’t always find a 1/3 or 2/3 power law relationship between curvature and velocity. That was kind of a challenge until I realized that the mathematical relationship between measures of R and V (and between C and A) contains another variable, D, so that the complete formula relating R to V is:

V = D^1/3 *R^1/3

and C to A is

A = D^1/3 *C2^/3

where is is |dXd²Y-d²XdY|.

RM: So I realized that if one does a log-log regression of R on V (or of C on A) the value of the coefficient that is found by the analysis will depend on how much of the variance in the criterion variable is due to the variable left out of the analysis, D. That is, the value of the estimate of the power coefficient that is found by regression analysis will be biased from its true value (1/3 or 2/3, per the equations above) if one of the variables that accounts for the variance in the criterion variable is omitted from the analysis.

RM: So, as you can see, my analysis of the power law has nothing to do with what the measures of curvature and velocity – R, V, C and A – measure about the trajectory. My analysis is based only on treating R, V, C and A as variables, as is done in power law research. In that research, regression analysis is used to determine how much of the variance in V (or A) can be accounted for by variance in R (or C). They find that the most variance in V (or A) is usually best accounted for by a 1/3 (or 2/3) power function of R (or C). They take this finding to mean that there is a biophysical constraint on the relationship between the curvature and the speed with which movement occurs through that curve. But my analysis shows that the power law finding has nothing to do with biology or physics. It is a statistical artifact; a result of failure to include in the statistical (regression) analysis used to determine the power law one of the variables (D) that contributes to the variance in the criterion variable (V or A).

RM: So explaining what the variables R, V, C and A measure is not really relevant to this analysis, nor does it disprove the analysis. The analysis is based on the observation that it is impossible to extract information about how purposeful movement trajectories are produced by measuring only properties of the movement trajectory itself. So it doesn’t matter what aspects of the movement trajectories are measured – measures of any two aspects of the movement will tell you nothing about how the movement is produced. But when the measures you use are R and V (or C and A) you will often see a power relationship between these variables (with a coefficient close to 1/3 or 2/4). But this is a statistical artifact – an illusion in the sense that the observed relationship does not show what it seems to show – how organisms vary the speed with which they go through curves. Organisms do vary the speed with which they go through curves, but the explanation of how they do this is control theory, not biophyisical constraints, as suggested by the power law.

Best regards

Rick

–

Richard S. Marken

“The childhood of the human race is far from over. We have a long way to go before most people will understand that what they do for others is just as important to their well-being as what they do for themselves.” – William T. Powers

–

Richard S. Marken

“The childhood of the human race is far from over. We have a long way to go before most people will understand that what they do for others is just as important to their well-being as what they do for themselves.” – William T. Powers

[_Boris_Hartman]

Alex.

Please don’t mess Rick’s RCT with real PCT (Powers). Rick and with him Powers ladies has a huge problem of continuing PCT. Rick was somehow the only alternatve as probably nobody wanted to take responsability for CSGnet conversations. I think that also Bill beleived that Rick can continue the CSGnet debates although it was obvious in the time when he was with us (and there were really quality conversations on CSGnet) that Rick is not reliable person as he is to much oscilating between PCT and RCT. I proved that at least 50 times also in the time when Bill was included in conversations and it was obviuos that Rick is wrong. But I don’t know how and why Powers family protect him like a Polar Bear although it is obviuous that he is not continuing or upgrading PCT but he is mostly trying to improve RCT. He has high gain for protecting his »own ass«. As many more people on the world do. After all they are LCS.

You noticed very good that Rick is »bullshiting« and that somehow »bullshiting« is protected in USA. I’m really sorry that you have to experience the whole »bullshit« that can be on this forum. But I’m waiting for LCS IV to come out and then we’ll see what will happen, if Rick will continue with his »bulshitting« and Powers ladies will continue to protect him.

Best,

Boris

···

From: Alex Gomez-Marin [mailto:agomezmarin@gmail.com]
Sent: Tuesday, September 06, 2016 6:36 PM
To: csgnet@lists.illinois.edu
Subject: Re: My Dinner with Andre

i think rick’s statement so far isn’t more than what he would have said before even knowing that the speed-curvature relation existed in humans and flies: the any invariant between output degrees of freedom is not behavior.

now, the question is: from what behavior does that invariant come from?

so, 2 months after my initial email, we are back to where we started (V=V and output=illusion). time to kick ass in the motor control literature with some juicy perceptual control insights…!!!

On Tuesday, 6 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.06.09.10]

[From Rick Marken (2016.09.05.1045)]

Martin Taylor (2016.09.04.16.00) –

RM: But the most important thing I learned from our discussion was that as radius of curvature, R, increases, curvature decreases! …

RM: [There is still a problem for me with the fact that the power relationship between curvature, measured as C (1/R), and angular velocity, measured as A (V/R), still seems to show an increase in velocity (A) with curvature (C) since larger values of C now mean greater curvature and larger values of A mean greater speed around a curve).

MT: These are two rather shocking statements, considering that both of the things you didn’t know are absolutely critical in Alex’s experiment, and yet you have been insisting for nearly two months that your analysis of the situation was the only correct one.

RM: Well, then you’ll be really shocked to know that I still think my analysis is correct…

I have never complained about the correctness of your mathematics that produced the tautology V=V. So far as I can see, it is perfectly correct, and the result is plausible.

Most long disputes are based in some kind of misunderstanding, and I wonder if this one might be another example. I think I know what you are claiming that I have been saying is wrong – to me it has seemed pretty clear, but I could have been wrong all this time. If we could be more sure we aren’t talking at cross-purposes, there might be a path forward to an agreement. It might be helpful if you could say in four lines or less of non-mathematical text just what it is that you think you are right about, because I’m pretty sure it isn’t that V=V.

No maths, just a short and clear statement of claim, please.

Martin

[_Boris_Hartman]

In the text bellow….

···

From: Richard Marken [mailto:rsmarken@gmail.com]
Sent: Saturday, September 10, 2016 11:52 PM
To: csgnet@lists.illinois.edu
Subject: Re: My Dinner with Andre

[From Rick Marken (2016.09.10.1450)]

On Wed, Sep 7, 2016 at 11:45 PM, Warren Mansell wmansell@gmail.com wrote:

WM: Exactly let’s all stick with this research question please!

“Given that an organism produces a particular trajectory, and that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is high, and what is being controlled that makes this happen?”

RM: Except for that last phase, that’s the research question I have answered (even if you don’t like the answer, it is an answer to that question). That last part – “what is being controlled that makes this happen?”-- assumes that the explanation is in terms of what variable is being controlled.

HB :

So what variable is being controlled ? If something happens in outer environment of orgaism than something in organism has to be controlled and that is the question, isn’t it ? But the problem I see is which »variable« you have in mind Rick. knowing you and your RCT  I’d say that you are approaching from the point of RCT so that »Behavior is Control« and that there is »Controlled variable in environment«. So i assume that your » terms of what variable is being controlled« is simply some »controlled variable outside organism«.

RM :

However, there is no reason to believe that control has anything to do with the observation of the power law. There is nothing in the power law that suggests that a variable is being maintained in a reference state (constant or variable) protected from disturbance.

HB :

As far as I understand »Power Law« is not showing any control outside organism, because there isn’t any. If I understand right …  power function take on any particular valuue when the correlation is high, and what is being controlled that makes this happen?"

HB :

Which »VARIABLE« by your oppinion Rick is being maintained in a reference state (constant or variable) protected from disturbance ???It seems Rick that you are promoting some »Controlled variable« in outside environment, so RCT is being promoted.

It seems that you are hanging on your RCT, which has nothing to do with PCT. It seems that you see some »controlled variable« in outside environment of organism which is »protected from disturbances« !!!??? and that behavior is some process of control that is »making trajectory« outside and is being under control »protected from disturbances«…. This is your RCT.

When you’ll stop with it ??? Â

WM: And what is being controlled is not the two dimensional dynamic path of distance from a target.

HB : Right. I agree Warren.

RM: How do you know? Actually, it seems highly likely that it’s precisely this dynamic path that is being controlled when people produce movement trajectories.

HB :

This is one thing that is sure not controlled…!!!

RM : Physics suggests that these trajectories are being produced in the face of disturbances. If it’s not the trajectories themselves that are controlled then what else could it be?

WM: That is cheating because it just begs the question of how that target trace occurred in the first place. We need scaffolding, not skyhooks…

HB :

What is being controlled is something in organism Rick. It’s not something outside. You have all the time problem with turning process of control from inside to outside. How many times did I suggested you to read Henry Yin article again. If you are asking what else could it be controlled beside »trajectory« outside organism, then Rick I don’t see any help for you. You are PCT blind. There are milions of control processes going on in organism and you are asking what else beside »trajectory« organism can be controlled by organism ??? What’s worng with you man…

<

RM: I think you mean that assuming that an observed movement trajectory is the result of a dynamically varying reference for the position of the moved entity (such as a cursor) is begging the question. But I don’t think it is. It’s proposing a falsifiable theory that explains what is observed.

HB : Are these two statements : above and under the same topics ?

RM : ….what we are seeing when people make twoo dimensional movements of a cursor on the screen is the dynamically varying reference state of cursor position.

HB . If those statements above are in contradiction, you are bluffing all along Rick. It seems that Warren was right and you are just repeating him in last statement, so that it looks like you made it on your own. I hiope you understand now what is behavior used for ? What kind of TCV should we use to discover that you are blluffing ???

Observed movement is always the result of varying references and varying perception. Is there any secret ?

Best,

Boris

The theory can be disproved by seeing whether it can account for the movement trajectory when disturbances are applied to the moved entity. I have done this, using a cursor as the moved entity and taking the observed movement of the cursor under disturbance as a reflection of the movement of the reference for cursor position. When this estimate of the reference is placed in a control model, moving the cursor in the face of the same disturbances that had been present when the person had moved the cursor, the model behaved exactly the same as the person. This would not have happened if the position of the cursor were not a controlled variable being controlled relative to the estimates reference.

RM: So according to my model (PCT) what we are seeing when people make two dimensional movements of a cursor on the screen is the dynamically varying reference state of cursor position. I’m sure this same model would apply to the movements made during cursive writing or when spacial patterns are traced out by moving a finger through space. Most of these movements will produce “power law” relationships between curvature and velocity with coefficients close to 1/3 (or 2/3) for the reasons given in my statistical analysis of the power law.

Best

Rick

On 8 Sep 2016, at 07:11, Alex Gomez-Marin agomezmarin@gmail.com wrote:

don’t confuse yourself and the readers again! rick, for your amazing derivation to be a power law, D should not depend mathematically on dX/dt, d2Y/dt, etc. period! aghhhhh…!!

so, again, i ask to the gurus of the revolution that will change biology and psychology and sociology: what is the organism controlling (larva and human) so as to produce such a speed-curvature constraint in the output?

On Thursday, 8 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

RM: The first step in the study of how organisms produce movement trajectories should be the determination of whether or not the trajectories that are observed are purposefully produced – whether or not the movement trajectory or some aspect thereof is a controlled variable.

That’s probably true, but it has nothing to do with the problem. Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you want to address, that’s great, but I thought we had all this time been talking about Alex’s question, which can be paraphrased as “Given that an organism produces a particular trajectory, and that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is high, and what is being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

Alex Gomez-Marin (2016.09.07.1134)

​AGM: Rick, I really really liked what you say in the last email until you jump from a conscious and clear explanation onto an ad hoc statement which is false: "It turns o

​​

ut

​​

that there is a mathematical relationship between the different measures of the controlled variable – curvature and velocity-- that perfectly accounts for the “power law” relationship between these variables that is observed in studies of movement trajectories.

​" FALSE FALSE FALSE! But you don’t care.

RM: I do care. But no one has shown me that what I’ve found is false. I would be grateful if you would try to show me again why my derivation is false. Again, I assume these are the formulae that can be used to compute V and R:

<mime-attachment.png>

RM: Replacing V^2 in the numerator for R I end up with the formula that everyone seems to think is wrong:

V = D^1/3 *R^1/3 (1)

where D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

RM: I think the algebra is unquestionably correct. But what also convinces me that this is a correct analysis is that I have replicated all the results reported in the power law papers using the above as the computational formulae for V and R above and equation (1) explains all the deviations of the observed power coefficients from 1/3.

RM: But I would like to know why you (and nearly everyone else apparently) thinks this mathematical analysis is false.

I don’t know anyone who has said it is false. I certainly haven’t, because it is demonstrably correct. It says V = V, because D is V³/R. It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how long. It’s irrelevant because the V in the formula for curvature is a purely arbitrary variable inserted only so that people can more easily think about movement along the trajectory, and it also helps one to visualize the concept of “angular velocity” (V(s)/R(s)). V(s) can take on any value at any point “s” on the curve and the algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary V(s), but with just one observation of how some organism speeded up and slowed down during one particular pass along the trajectory. Since the algebra works for any V(s) at all, it is tells you nothing about this particular V(s). We have to look elsewhere for the reason why this V(s) happened to be the function of “s” that was observed.

Martin

–

Richard S. Marken

“The childhood of the human race is far from over. We have a long way to go before most people will understand that what they do for others is just as important to their well-being as what they do for themselves.” – William T. Powers

[Alex_Gomez-Marin]

[From Alex Gomez-Marin (2016.09.11.1157)]

RM: That last part – “what is being controlled that makes this happen?”-- assumes that the explanation is in terms of what variable is being controlled. However, there is no reason to believe that control has anything to do with the observation of the power law. There is nothing in the power law that suggests that a variable is being maintained in a reference state (constant or variable) protected from disturbance.

AGM: So the power law, has now been degraded (ad hoc) to even less than a behavioral illusion?? I mean, how can such a non-trivial covariance of speed and curvature stem for no reason and from nowhere? I accept that we don’t know yet what the animal is trying to control while generating those trajectories (still, my original question, which remains unanswered), but now saying that the biological power law (cause it is not pure maths nor physics! — even for those who don’t knoww maths nor physics!!) is a motor pattern that emerges in humans and flies (but doesn’t in fish or walking mice) but that doesn’t deserve explanation is simply another of these Rick-like claims that keep on surprising me, to put it mildly. Show it! Argue for it! Don’t claim it ex-PCT-cathedra!

···

On Sat, Sep 10, 2016 at 11:52 PM, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2016.09.10.1450)]

On Wed, Sep 7, 2016 at 11:45 PM, Warren Mansell wmansell@gmail.com wrote:

WM: Exactly let’s all stick with this research question please!

“Given that an organism produces a particular trajectory, and that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is high, and what is being controlled that makes this happen?”

RM: Except for that last phase, that’s the research question I have answered (even if you don’t like the answer, it is an answer to that question). That last part – “what is being controlled that makes this happen?”-- assumes that the explanation is in terms of what variable is being controlled. However, there is no reason to believe that control has anything to do with the observation of the power law. There is nothing in the power law that suggests that a variable is being maintained in a reference state (constant or variable) protected from disturbance.

Â

WM: And what is being controlled is not the two dimensional dynamic path of distance from a target.

RM: How do you know? Actually, it seems highly likely that it’s precisely this dynamic path that is being controlled when people produce movement trajectories. Physics suggests that these trajectories are being produced in the face of disturbances. If it’s not the trajectories themselves that are controlled then what else could it be?

WM: That is cheating because it just begs the question of how that target trace occurred in the first place. We need scaffolding, not skyhooks…

RM: I think you mean that assuming that an observed movement trajectory is the result of a dynamically varying reference for the position of the moved entity (such as a cursor) is begging the question. But I don’t think it is. It’s proposing a falsifiable theory that explains what is observed. The theory can be disproved by seeing whether it can account for the movement trajectory when disturbances are applied to the moved entity. I have done this, using a cursor as the moved entity and taking the observed movement of the cursor under disturbance as a reflection of the movement of the reference for cursor position. When this estimate of the reference is placed in a control model, moving the cursor in the face of the same disturbances that had been present when the person had moved the cursor, the model behaved exactly the same as the person. This would not have happened if the position of the cursor were not a controlled variable being controlled relative to the estimates reference.Â

RM: So according to my model (PCT) what we are seeing when people make two dimensional movements of a cursor on the screen is the dynamically varying reference state of cursor position. I’m sure this same model would apply to the movements made during cursive writing or when spacial patterns are traced out by moving a finger through space. Most of these movements will produce “power law” relationships between curvature and velocity with coefficients close to 1/3 (or 2/3) for the reasons given in my statistical analysis of the power law.

Best

Rick

Â

On 8 Sep 2016, at 07:11, Alex Gomez-Marin agomezmarin@gmail.com wrote:

don’t confuse yourself and the readers again! rick, for your amazing derivation to be a power law, D should not depend mathematically on dX/dt, d2Y/dt, etc. period! aghhhhh…!!

so, again, i ask to the gurus of the revolution that will change biology and psychology and sociology: what is the organism controlling (larva and human) so as to produce such a speed-curvature constraint in the output?

On Thursday, 8 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

That's probably true, but it has nothing to do with the problem.

Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you

want to address, that’s great, but I thought we had all this time
been talking about Alex’s question, which can be paraphrased as
“Given that an organism produces a particular trajectory, and that
under some conditions the velocity of motion along the trajectory at
a point is correlated with a power function of the local curvature
at that point, under what conditions does that power function take
on any particular value when the correlation is high, and what is
being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

I don't know anyone who has said it is false. I certainly haven't,

because it is demonstrably correct. It says V = V, because D is V³ /R.
It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how

long. It’s irrelevant because the V in the formula for curvature is
a purely arbitrary variable inserted only so that people can more
easily think about movement along the trajectory, and it also helps
one to visualize the concept of “angular velocity” (V(s)/R(s)).Â
V(s) can take on any value at any point “s” on the curve and the
algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary

V(s), but with just one observation of how some organism speeded up
and slowed down during one particular pass along the trajectory.
Since the algebra works for any V(s) at all, it is tells you nothing
about this particular V(s). We have to look elsewhere for the reason
why this V(s) happened to be the function of “s” that was observed.

Martin

–
Richard S. MarkenÂ

“The childhood of the human race is far from over. We
have a long way to go before most people will understand that what they do for
others is just as important to their well-being as what they do for
themselves.” – William T. Powers

    RM: The first step in the study of how

organisms produce movement trajectories should be the
determination of whether or not the trajectories that are
observed are purposefully produced – whether or not the
movement trajectory or some aspect thereof is a controlled
variable.

                Â Alex

Gomez-Marin (2016.09.07.1134)

​​

​​

                ​AGM: Rick, I really really

liked what you say in the last email until you jump
from a conscious and clear explanation onto an ad
hoc statement which is false: “** It
turns o ut**** that
there is a mathematical relationship**
between the different measures of the controlled
variable – curvature and velocity-- ** that
perfectly accounts for the “power law”
relationship** between these variables that
is observed in studies of movement
trajectories.Â
​”
FALSE FALSE FALSE! But you don’t care.

          RM: I do care. But no one has shown me that what I've

found is false. I would be grateful if you would try to
show me again why my derivation is false. Again, I assume
these are the formulae that can be used to compute V and
R:

<mime-attachment.png>

          RM: Replacing V^2 in the numerator for R I end up with

the formula that everyone seems to think is wrong:Â

              V =

 D^1/3 *R^{1/3 Â}     (1)
  Â
                    Â

            where

D is |dX/dtd²Y/dt -d²X/dtdY/dt|Â ,Â

          RM: I think the algebra is unquestionably correct. But

what also convinces me that this is a correct analysis is
that I have replicated all the results reported in the
power law papers using the above as the computational
formulae for V and R above and equation (1) explains all
the deviations of the observed power coefficients from
1/3.Â

          RM: But I would like to know why you (and nearly

everyone else apparently) thinks this mathematical
analysis is false.Â

[MartinT]

[Martin Taylor 2016.09.11.10.32]

[From Rick Marken (2016.09.10.1450)]

One problem in this whole discussion is that words are being used in

two different ways while being treated as being the same. It’s
similar to the mathematical sleigh of hand that allows you to prove
that 1 = 2 by a subtly hidden division by zero.

Here, there are two such interlinked terms: "trajectory" and "power

law". Both the American Random House and the English Oxford
dictionaries define “trajectory” as a shape. It isn’t a dynamic
category, in that it contains no sense of time or speed, even though
the shape was produced by a moving body. Rick accepted that in his
initial model, which showed how a trajectory (shape) could be
reproduced by a control system of two control units that followed a
moving target as it traced the shape of a trajectory.

"Power Law" is also being used in two different ways, one of which

deals with shape, while the other deals with motion. Alex’s question
quoted above as I paraphrased it, has to do with motion. Rick’s
(in)famous equation has to do with shape and shape alone, despite
his ingenious extraction of a variable called “V” from both sides of
the equation. Shape and motion are unrelated by any physical
requirement until some other consideration (e.g. gravity for
planetary orbits) is introduced.

···

On Wed, Sep 7, 2016 at 11:45 PM,
Warren Mansell wmansell@gmail.com wrote:

              WM: Exactly let's all stick with this research

question please!

                  "Given

that an organism produces a particular trajectory,
and that under some conditions the velocity of
motion along the trajectory at a point is
correlated with a power function of the local
curvature at that point, under what conditions
does that power function take on any particular
value when the correlation is high, and what is
being controlled that makes this happen?"

          RM: Except for that last phase, that's the research

question I have answered (even if you don’t like the
answer, it is an answer to that question). That last part
– “what is being controlled that makes this happen?”–
assumes that the explanation is in terms of what variable
is being controlled. However, there is no reason to
believe that control has anything to do with the
observation of the power law. There is nothing in the
power law that suggests that a variable is being
maintained in a reference state (constant or variable)
protected from disturbance.

                WM: And what is being controlled is not the two

dimensional dynamic path of distance from a target.

          RM: How do you know? Actually, it seems highly likely

that it’s precisely this dynamic path that is being
controlled when people produce movement trajectories.
Physics suggests that these trajectories are being
produced in the face of disturbances. If it’s not the
trajectories themselves that are controlled then what else
could it be?

                WM: That is cheating because it just begs the

question of how that target trace occurred in the
first place. We need scaffolding, not skyhooks…

          RM: I think you mean that assuming that an observed

movement trajectory is the result of a dynamically varying
reference for the position of the moved entity (such as a
cursor) is begging the question. But I don’t think it is.
It’s proposing a falsifiable theory that explains what is
observed. The theory can be disproved by seeing whether it
can account for the movement trajectory when disturbances
are applied to the moved entity. I have done this, using a
cursor as the moved entity and taking the observed
movement of the cursor under disturbance as a reflection
of the movement of the reference for cursor position. When
this estimate of the reference is placed in a control
model, moving the cursor in the face of the same
disturbances that had been present when the person had
moved the cursor, the model behaved exactly the same as
the person. This would not have happened if the position
of the cursor were not a controlled variable being
controlled relative to the estimates reference.

          RM: So according to my model (PCT) what we are seeing

when people make two dimensional movements of a cursor on
the screen is the dynamically varying reference state of
cursor position. I’m sure this same model would apply to
the movements made during cursive writing or when spacial
patterns are traced out by moving a finger through
space. Most of these movements will produce “power law”
relationships between curvature and velocity with
coefficients close to 1/3 (or 2/3) for the reasons given
in my statistical analysis of the power law.

Best

Rick

On 8 Sep 2016, at 07:11, Alex Gomez-Marin <agomezmarin@gmail.com >
wrote:

                  don't confuse yourself and the readers

again! rick, for your amazing derivation to be a
power law, D should not depend mathematically on
dX/dt, d2Y/dt, etc. period! aghhhhh…!!

                    so, again, i ask to the gurus of the

revolution that will change biology and
psychology and sociology: what is the organism
controlling (larva and human) so as to produce
such a speed-curvature constraint in the output?

                    On Thursday, 8 September 2016, Martin Taylor

<mmt-csg@mmtaylor.net >
wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

                          [From Rick Marken

(2016.09.07.1420)]

                        That's probably true, but it has nothing to

do with the problem. Nobody has asked how
organisms produce movement trajectories.

                        If how organisms produce particular

trajectories is a problem you want to
address, that’s great, but I thought we had
all this time been talking about Alex’s
question, which can be paraphrased as “Given
that an organism produces a particular
trajectory, and that under some conditions
the velocity of motion along the trajectory
at a point is correlated with a power
function of the local curvature at that
point, under what conditions does that power
function take on any particular value when
the correlation is high, and what is being
controlled that makes this happen?”

                          [From Rick Marken

(2016.09.07.1710)]

I don’t know anyone who has said it is
false. I certainly haven’t, because it is
demonstrably correct. It says V = V, because
D is V³/R. It’s just irrelevant.

                        Which is what everyone has been telling you

for goodness knows how long. It’s irrelevant
because the V in the formula for curvature
is a purely arbitrary variable inserted only
so that people can more easily think about
movement along the trajectory, and it also
helps one to visualize the concept of
“angular velocity” (V(s)/R(s)). V(s) can
take on any value at any point “s” on the
curve and the algebra still works. V = V
everywhere.

                        The question being asked has to do not with

a generic and arbitrary V(s), but with just
one observation of how some organism speeded
up and slowed down during one particular
pass along the trajectory. Since the algebra
works for any V(s) at all, it is tells you
nothing about this particular V(s). We have
to look elsewhere for the reason why this
V(s) happened to be the function of “s” that
was observed.

                        Martin

–
Richard S. Marken

                                    "The childhood of the human

race is far from over. We
have a long way to go before
most people will understand that
what they do for
others is just as important to
their well-being as what they do
for
themselves." – William T.
Powers

                            RM: The first

step in the study of how organisms
produce movement trajectories should be
the determination of whether or not the
trajectories that are observed are
purposefully produced – whether or not
the movement trajectory or some aspect
thereof is a controlled variable.

                                         Alex

Gomez-Marin
(2016.09.07.1134)

​​

​​

                                        ​AGM: Rick, I really

really liked what you say in
the last email until you
jump from a conscious and
clear explanation onto an ad
hoc statement which is
false: “** It
turns o ut**** that
there is a
mathematical
relationship**
between the different
measures of the
controlled variable –
curvature and velocity–
** that perfectly
accounts for the
“power law”
relationship**
between these variables
that is observed in
studies of movement
trajectories.
​”
FALSE FALSE FALSE! But you
don’t care.

                                  RM: I do care. But no one has

shown me that what I’ve found is
false. I would be grateful if you
would try to show me again why my
derivation is false. Again, I
assume these are the formulae that
can be used to compute V and R:

<mime-attachment.png>

                                  RM: Replacing V^2 in the

numerator for R I end up with the
formula that everyone seems to
think is wrong:

                                      V =

D^1/3 *R^1/3
(1)

                                    where

D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

                                  RM: I think the algebra is

unquestionably correct. But what
also convinces me that this is a
correct analysis is that I have
replicated all the results
reported in the power law papers
using the above as the
computational formulae for V and R
above and equation (1) explains
all the deviations of the observed
power coefficients from 1/3.

                                  RM: But I would like to know

why you (and nearly everyone else
apparently) thinks this
mathematical analysis is false.

[rsmarken]

[From Rick Marken (2016.09.11.1100)]

···

Alex Gomez-Marin (2016.09.11.1157)

AGM: So the power law, has now been degraded (ad hoc) to even less than a behavioral illusion??

RM: The power law is an “illusion” only if you see it as a relationship between a stimulus (causal or constraining) variable (curvature) and a response (effect or output) variable (velocity).

AGM:…I accept that we don’t know yet what the animal is trying to control while generating those trajectories

RM:I think we can get a pretty good idea. What is controlled depends on the behavioral situation. A person who is doing cursive writing with a pen is surely controlling (among other things) the position of the pen; a person moving their finger around in air or water is surely controlling (among other things) the position of the finger. A fly larva moving to food is probably controlling for increasing the magnitude of the sensory effects of the food. So the controlled variables are different in different situations. This means that sometimes the observed movement trajectory is itself controlled (as in writing or moving a finger around) and sometimes it is a side effect of controlling something else (as when a fly larvae navigates to food).

It’s really not that hard to guess what variables organisms are likely to be controlling. The hard part is making the description of these variables precise. For example, in the ball catching research it was pretty obvious that fielders are controlling some aspect of the optical trajectory of the ball. The interesting question (from a PCT perspective) is “exactly what aspect?”. There were basically three hypotheses about the aspect of the optical trajectory that is controlled: the linearity of the optical trajectory, the optical acceleration of the ball or the optical velocity of the ball. Using modeling we were able to show that optical velocity comes closest to representing the aspect of the sensory input (the perceptual variable) that is controlled.

AGM: …but now saying that the biological power law…is a motor pattern that emerges in humans and flies (but doesn’t in fish or walking mice) but that doesn’t deserve explanation

RM: It certainly does deserve explanation; and I’ve explained it; it is simply a statistical side effect of analyzing any curved two-dimensional movement pattern, whether it is produced intentionally (as as the movements produced when writing and moving a finger around) or not (as in the movement of the fly larvae and the planets).

Best

Rick

is simply another of these Rick-like claims that keep on surprising me, to put it mildly. Show it! Argue for it! Don’t claim it ex-PCT-cathedra!

–
Richard S. Marken

“The childhood of the human race is far from over. We
have a long way to go before most people will understand that what they do for
others is just as important to their well-being as what they do for
themselves.” – William T. Powers

On Sat, Sep 10, 2016 at 11:52 PM, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2016.09.10.1450)]

On Wed, Sep 7, 2016 at 11:45 PM, Warren Mansell wmansell@gmail.com wrote:

WM: Exactly let’s all stick with this research question please!

“Given that an organism produces a particular trajectory, and that under some conditions the velocity of motion along the trajectory at a point is correlated with a power function of the local curvature at that point, under what conditions does that power function take on any particular value when the correlation is high, and what is being controlled that makes this happen?”

RM: Except for that last phase, that’s the research question I have answered (even if you don’t like the answer, it is an answer to that question). That last part – “what is being controlled that makes this happen?”-- assumes that the explanation is in terms of what variable is being controlled. However, there is no reason to believe that control has anything to do with the observation of the power law. There is nothing in the power law that suggests that a variable is being maintained in a reference state (constant or variable) protected from disturbance.

WM: And what is being controlled is not the two dimensional dynamic path of distance from a target.

RM: How do you know? Actually, it seems highly likely that it’s precisely this dynamic path that is being controlled when people produce movement trajectories. Physics suggests that these trajectories are being produced in the face of disturbances. If it’s not the trajectories themselves that are controlled then what else could it be?

WM: That is cheating because it just begs the question of how that target trace occurred in the first place. We need scaffolding, not skyhooks…

RM: I think you mean that assuming that an observed movement trajectory is the result of a dynamically varying reference for the position of the moved entity (such as a cursor) is begging the question. But I don’t think it is. It’s proposing a falsifiable theory that explains what is observed. The theory can be disproved by seeing whether it can account for the movement trajectory when disturbances are applied to the moved entity. I have done this, using a cursor as the moved entity and taking the observed movement of the cursor under disturbance as a reflection of the movement of the reference for cursor position. When this estimate of the reference is placed in a control model, moving the cursor in the face of the same disturbances that had been present when the person had moved the cursor, the model behaved exactly the same as the person. This would not have happened if the position of the cursor were not a controlled variable being controlled relative to the estimates reference.

RM: So according to my model (PCT) what we are seeing when people make two dimensional movements of a cursor on the screen is the dynamically varying reference state of cursor position. I’m sure this same model would apply to the movements made during cursive writing or when spacial patterns are traced out by moving a finger through space. Most of these movements will produce “power law” relationships between curvature and velocity with coefficients close to 1/3 (or 2/3) for the reasons given in my statistical analysis of the power law.

Best

Rick

On 8 Sep 2016, at 07:11, Alex Gomez-Marin agomezmarin@gmail.com wrote:

don’t confuse yourself and the readers again! rick, for your amazing derivation to be a power law, D should not depend mathematically on dX/dt, d2Y/dt, etc. period! aghhhhh…!!

so, again, i ask to the gurus of the revolution that will change biology and psychology and sociology: what is the organism controlling (larva and human) so as to produce such a speed-curvature constraint in the output?

On Thursday, 8 September 2016, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.09.07.23.15]

Answering two e-mails in one.

[From Rick Marken (2016.09.07.1420)]

That's probably true, but it has nothing to do with the problem.

Nobody has asked how organisms produce movement trajectories.

If how organisms produce particular trajectories is a problem you

want to address, that’s great, but I thought we had all this time
been talking about Alex’s question, which can be paraphrased as
“Given that an organism produces a particular trajectory, and that
under some conditions the velocity of motion along the trajectory at
a point is correlated with a power function of the local curvature
at that point, under what conditions does that power function take
on any particular value when the correlation is high, and what is
being controlled that makes this happen?”

[From Rick Marken (2016.09.07.1710)]

I don't know anyone who has said it is false. I certainly haven't,

because it is demonstrably correct. It says V = V, because D is V³ /R.
It’s just irrelevant.

Which is what everyone has been telling you for goodness knows how

long. It’s irrelevant because the V in the formula for curvature is
a purely arbitrary variable inserted only so that people can more
easily think about movement along the trajectory, and it also helps
one to visualize the concept of “angular velocity” (V(s)/R(s)).
V(s) can take on any value at any point “s” on the curve and the
algebra still works. V = V everywhere.

The question being asked has to do not with a generic and arbitrary

V(s), but with just one observation of how some organism speeded up
and slowed down during one particular pass along the trajectory.
Since the algebra works for any V(s) at all, it is tells you nothing
about this particular V(s). We have to look elsewhere for the reason
why this V(s) happened to be the function of “s” that was observed.

Martin

Richard S. Marken

“The childhood of the human race is far from over. We
have a long way to go before most people will understand that what they do for
others is just as important to their well-being as what they do for
themselves.” – William T. Powers

–

    RM: The first step in the study of how

organisms produce movement trajectories should be the
determination of whether or not the trajectories that are
observed are purposefully produced – whether or not the
movement trajectory or some aspect thereof is a controlled
variable.

                 Alex

Gomez-Marin (2016.09.07.1134)

​​

​​

                ​AGM: Rick, I really really

liked what you say in the last email until you jump
from a conscious and clear explanation onto an ad
hoc statement which is false: “** It
turns o ut**** that
there is a mathematical relationship**
between the different measures of the controlled
variable – curvature and velocity-- ** that
perfectly accounts for the “power law”
relationship** between these variables that
is observed in studies of movement
trajectories.
​”
FALSE FALSE FALSE! But you don’t care.

          RM: I do care. But no one has shown me that what I've

found is false. I would be grateful if you would try to
show me again why my derivation is false. Again, I assume
these are the formulae that can be used to compute V and
R:

<mime-attachment.png>

          RM: Replacing V^2 in the numerator for R I end up with

the formula that everyone seems to think is wrong:

              V =

D^1/3 *R^1/3 (1)

            where

D is |dX/dtd²Y/dt -d²X/dtdY/dt| ,

          RM: I think the algebra is unquestionably correct. But

what also convinces me that this is a correct analysis is
that I have replicated all the results reported in the
power law papers using the above as the computational
formulae for V and R above and equation (1) explains all
the deviations of the observed power coefficients from
1/3.

          RM: But I would like to know why you (and nearly

everyone else apparently) thinks this mathematical
analysis is false.